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Cited by 48Quantum Computing Algorithms and ArchitectureError Correcting Code TechniquesQuantum Information and Cryptography

Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead

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Higgott, Oscar, Breuckmann, Nikolas P.·2021·Physical Review X
DOI 10.1103/physrevx.11.031039
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Abstract

We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes.By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance.Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarizing noise from 0.67% to 0.81%.The threshold increases further under a circuit-level noise model with small finite bias, up to 2.22% for infinite bias.Furthermore, we construct families of finite-rate subsystem low-density parity-check codes with threequbit check operators and optimal-depth parity-check measurement schedules.To the best of our knowledge, these finite-rate subsystem codes outperform all known codes at circuit-level depolarizing error rates as high as 0.2%, where they have a qubit overhead that is 4.3× lower than the most efficient version of the surface code and 5.1× lower than the subsystem toric code.Their threshold and pseudothreshold exceeds 0.42% for circuit-level depolarizing noise, increasing to 2.4% under infinite bias using gauge fixing.

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  • It was previously believed that outperforming the surface code for realistic noise models including memory, gate and state preparation and measurement errors may require very large LDPC codes with more than 10,000 physical qubits.

    “However, it was previously believed that outperforming the surface code for realistic noise models including memory, gate and state preparation and measurement errors may require very large LDPC codes with more than 10,000 physical qubits31.”

    From High-threshold and low-overhead fault-tolerant quantum memory (2024) · cites this paper as [31]

    The Introduction says that prior LDPC codes had not been shown to reduce qubit overhead relative to the surface code once circuit-level noise was included. The Noise models section confirms that the paper considers gate, idle-qubit, state-preparation, and measurement errors. But the paper does not say that outperforming the surface code was previously believed to require more than 10,000 physical qubits; its Results instead describe a code using 18,816 qubits, without presenting that number as a prior requirement. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Higgott and Breuckmann demonstrated that this lost information can be recovered using schedule-induced gauge fixing.

    “Higgott and Breuckmann demonstrated [112] that this lost information can be recovered using schedule-induced gauge fixing.”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [112]

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Cited by

Sorted by citations

Authors
Higgott, O., & Breuckmann, N. P.
Affiliations
University College London (GB)
ORCID
Venue
Physical Review X
Publisher
American Physical Society (APS)
Published
2021-08-19
Volume
11
Issue
3
ISSN
2160-3308 (ISSN-L)
DOI
10.1103/physrevx.11.031039
OpenAlex
W3092764718
Cited by
48
References
10
Citations by year
2026: 3 · 2025: 9 · 2024: 16 · 2023: 10 · 2022: 8 · 2021: 2
FWCI
3.03
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review X (publishedVersion, cc-by)
  • Bristol Research (University of Bristol) (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • UCL Discovery (University College London) (submittedVersion)
  • Explore Bristol Research (submittedVersion, cc-by)
  • arXiv (Cornell University)
  • Bulletin of the American Physical Society
Funders
  • Engineering and Physical Sciences Research Council (EP/L015242/1)
  • UCLQ Fellowship
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
subsystem codes, gauge fixing, quantum error correction, threshold, LDPC codes, decoding, qubit overhead, depolarizing noise, biased noise

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